nctm standards: 3, 6, 8, 9, 10. 1.1 points, lines, & planes pointlineplane definition model...

NCTM Standards: 3, 6, 8, 9, 10

1.1 Points, Lines, & PlanesPoint Line Plane

Definition

Model

Drawn

Named By:

Facts

Words/

Symbols

As a dot With an arrow at each end

A location in space, represented by a dot

A set of points that extends without end in two opposite directions

A set of points that extends in four directions without end

As a parallelogram

A capital block letter

Two points on the line or a lower-case cursive

A capital cursive letter or 3 noncollinear * points

Has no shape or size

Has immeasurable length, but no width or thickness

Has length & width, but no thickness

Point P

P

Line n, line AB, line BA

BAor AB

Plane T, plane XYZ, plane XZY, Plane YXZ, Plane YZX, etc.

* Noncollinear: three or more points not in a straight line

SOLUTION

EXAMPLE 1 Name points, lines, and planes

b. Name three points that are collinear.Name four points that are coplanar.

a. Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.

a. Give two other names for PQ and for plane R.

b. Points S, P, and T lie on the same line, so they are collinear. Points S, P, T,and V lie in the same plane, so they are coplanar.

GUIDED PRACTICE for Example 1

ANSWER

Other names for ST are TS and PT. Point V is not coplanar with points Q,S and T

1. Use the diagram in Example 1. Give two other names for ST . Name a point that is not coplanar with points Q, S, and T.

EXAMPLE 3 Sketch intersections of lines and planes

a. Sketch a plane and a line that is in the plane.

b. Sketch a plane and a line that does not intersect the plane.

c. Sketch a plane and a line that intersects the plane at a point.

SOLUTION

a. b. c.

EXAMPLE 4 Sketch intersections of planes

Sketch two planes that intersect in a line.

SOLUTION

Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden.

STEP 2

Draw: the line of intersection.STEP 3

Draw: a vertical plane. Shade the plane.

STEP 1

GUIDED PRACTICE for Examples 3 and 4

4. Sketch two different lines that intersect a plane at the same point.

Use the diagram at the right.

5. Name the intersection of PQ and line k.

ANSWER Point M

ANSWER

GUIDED PRACTICE

6. Name the intersection of plane A and plane B.

7. Name the intersection of line k and plane A.

ANSWER Line K

ANSWER Line K

G

H

J

K

L

M

Q

•T•U•R

Space

A boundless, three-dimensional set of all points. Space can contain lines & planes.

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